A town has a population of 1 million. The average electric power needed per person is 300 W . A reactor is designed to supply power to this town, with an aimed efficiency of 25 % for converting thermal power into electric power. Assuming an average of 200 MeV of thermal energy is released from each fission event, and that the fission occurs largely through ²³⁵ U , at what rate will the amount of ²³⁵ U decrease? Expre

Step-by-step solution

Total electric power required by the town: P_e = 10^6 300 W = 3 10^8 W Since the efficiency of converting thermal power to electric power is 25 % , the total thermal power required is: P_ th = P_e 0.25 = 3 10^8 0.25 = 1.2 10^9 W = 1.2 10^9 J/s Energy released per fission of ²³⁵ U is: E = 200 MeV = 200 10^6 1.6 10⁻¹⁹ J = 3.2 10⁻¹¹ J The number of fissions occurring per second is: dn dt = P_ th E = 1.2 10^9 3.2 10⁻¹¹ = 3.75 10¹⁹ s ⁻¹ The number of fissions per day is: N = 3.75 10¹⁹ (24 60 60) = 3.75 10¹⁹ 86400 = 3.24